A quadrature signal is a complex signal with two components, one of which may be interpreted as a real component, and the other of which may be interpreted as an imaginary component. By convention, the two components are named I, for in phase signal, and Q, for quadrature phase signal, respectively. These components may be generated from a single real signal by phase-shifted mixing or sampling. Quadrature signal processing and sampling are widely employed in many fields, including precision metrology and optical velocimetry, detection and ranging systems such as radar, sonar, and lidar, and communications technology. The use of quadrature signal processing may produce many system advantages, including reduced cost and size, and increased flexibility of function. In radar and sonar systems, for example, the use of quadrature signals allows determination of polarity of Doppler shift and, consequently, the direction of motion of the target—that is, away from, or towards, the observer. In communications systems, for example, multiple modulation modes may be implemented in the same hardware by varying the manner of baseband signal processing, when quadrature sampling is used.
In practice, however, quadrature signals invariably have at least some amplitude error and phase error, that can act to reduce system performance. In radio systems, for example, the I and Q quadrature signals may be generated by a pair of mixers whose local oscillators are phase-shifted by 90.0°. Alternatively, if sampling is used, samplers whose sample clocks are phase-shifted by 90.0°, together with lowpass filtering for analog systems or decimation for digital systems, may be employed to generate the I and Q signals. If the processing gains in the I and Q signal paths of such quadrature signal generators are not identical, the resulting I and Q signals are said to have amplitude imbalance. If the sampling phase for the I and Q signals is not exactly 90.0°, they are said to have phase imbalance. These errors are collectively termed quadrature signal imbalance. At a system level, quadrature signal imbalance may be manifested as spectral images, distortion, and increased bit error rates, for example. Some degree of quadrature signal imbalance arises naturally in all practical applications.